Train A leaves station M at 7:40 AM and reaches station N at 2:40 PM on the same day. Train B leaves station N at 9:40 AM and reaches station M at 2:40 PM on the same day. Find the time when Trains A and B meet.

Correct option is D

Given:

Train A leaves station M at 7:40 AM and reaches station N at 2:40 PM on the same day.
Train B leaves station N at 9:40 AM and reaches station M at 2:40 PM on the same day.

Solution:

Calculate the total time of travel for each train:
- Train A's total travel time is 7 hours (from 7:40 AM to 2:40 PM).
- Train B's total travel time is 5 hours (from 9:40 AM to 2:40 PM).

Distance = LCM of 7, 5 = 35  

Speed of A = $$\frac{35}{7} = 5$$ unit/hour

Speed of B = $$\frac{35}{5} = 7$$ unit/hour

​In first 2 hour the distance cover by A  = $$5\times 2$$  = 10 unit

Reaming distance the both cover = $$\frac{35- 10}{2} = \frac{25}{5 +7}$$ hours  = $$\frac{25}{12} = 2 \ hours +\frac{1}{12}\times 60 \ minutes$$  = 2 hours + 5 minutes

They will meet = 9 : 40 AM + 2 hours + 5 minutes = 11 : 45 Am